(4) The contributions to form factor
\(F_{0}^{B_{c}{\rightarrow }B_{s}}(0)\)  from different region of
\({\alpha }_{s}/{\pi }\)  is displayed in Fig.REF ,
where \(e^{-S}\)  \({\ne }\)  1 (\(=\)  1) denote results
with (without) the Sudakov factor;
\(b_{i}\)  is the conjugate variable of the
transverse moment \(k_{i{\perp }}\) ;
\({\alpha }\)  [see Eq.(REF )] and
\({\beta }\)  [see Eq.() and Eq.()]
are the virtuality of the internal gluon and quark,
respectively.
From Fig.REF (a) we can see that if one choose
the virtuality of the internal gluon and quark as the
typical scale, the contribution to form factor
from \({\alpha }_{s}/{\pi }\)  \(<\)  \(0.3\)  region is less than 40%,
that is to say, the hard and soft contributions to the
form factor have the same behavior. This is the QCDF's
viewpoint of that the form factor is not fully calculable
in the hard scattering picture with the perturbation
theory and that the form factor should be regarded as
a nonperturbative quantity [1]}.
From Fig.REF (b) we can see that by keeping the
quark transverse momentum \(k_{T}\) , and employing the
Sudakov factors to suppress the kinematic configuration
when both longitudinal and transverse momentum are soft,
the contribution to form factor from
\({\alpha }_{s}/{\pi }\)  \(<\)  \(0.3\)  region is about 90% and
the percentage of contribution from large
\({\alpha }_{s}/{\pi }\)  region is small.
Our study also shows that besides retaining the quark
transverse momentum \(k_{\perp }\)  to smear the endpoint
divergence behavior and using the Sudakov factor to
suppress the nonperturbative contribution in large \(b\) 
region [2]}, as the discussion in [3]},
the choice of the hard scale is one of the important
ingredients of the pQCD approach, which deserve much attention.
If the scale \(t\)  is chosen as Eq.(REF ),
then it shows that most of the contributions come
from the \({\alpha }_{s}/{\pi }\)  \(<\)  0.3 region,
implying that the pQCD approach is applicable to
the \(B_{c}\)  \({\rightarrow }\)  \(B\)  transition form factors.
Of course, there are some controversies, even suspicion,
about the suppression mechanism of the Sudakov factor
on the nonperturbative contribution, about the choice
of the hard scale and so on. The deeper discussion of
these problems is needed and should be preformed, but
beyond the scope of this paper.
